Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination:

$x+y=7$, $5x+12y=7$

• A. $x=13$ and $y=5$
• B. $x=11$ and $y=-4$
• C. $x=7$ and $y=-2$
• D. $x=5$ and $y=7$

Answer 1

The correct option is B $x=11$ and $y=-4$

Multiply the equation $x+y=7$ by $5$ to make the coefficients of $x$ equal. Then we get the equations:

$5x+5y=\mathrm{35.........}\left(1\right)$

$5x+12y=\mathrm{7.........}\left(2\right)$

Subtract Equation (2) from Equation (1) to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(5x-5x)+(5y-12y)=35-7$

i.e. $7y=-28$

i.e. $y=-4$

Substituting this value of $y$ in the equation $x+y=7$, we get

$x-4=7$

i.e. $x=11$

Hence, the solution of the equations is $x=11,y=-4$.